Due Feb 24, 2:59 AM EST
Suppose we have 7 disjoint datasets and each dataset contains 12 data entries. How many data entries do we have in total?
This is correct!
We can think of this in the following way. To pick a data entry we have to make two sequential choices: first we need to pick a dataset and then one data entry from it. And we are actually counting pairs of these choices. We can make the first choice in 7 ways and the second choice in 12 ways. Then by the product rule we have 7x12=84 possible choices in total.
What is the number of segments in the picture below? Each segment joins two circles.

This is correct! Each circle on the top is connected to each circle on the bottom. So to pick a segment we need to pick one circle on the top and one circle on the bottom. There are 6 circles on the top and 7 circles on the bottom. So by the rule of product the number of segments is 6×7=42